Corrected radius

All reciprocal lattice levels and all angles of oscillation can be dealt with in this way, care being taken always to use the correct radius for the circle of contact. In the same way, if for any purpose it is desired to know at what angle any plane reflects, if is only neeessary to draw... 

It follows that an equation of Bom type, but based on different physical principles (Eq. 56) is a good approximation for the continuum energy in dipolar liquids up to the onset of dielectric saturation at x = 3, provided it is integrated from an appropriate distance somewhat less than that of the superdipole center of the innermost solvation shell from the central ion. This corrected radius will differ from the distance from the ion to the dipole centers of the solvation shell under consideration by about 50% more than the radius of a water molecule. 

Corrected radius equal to r + used in the modified Born expression, Eq. (4)... 

Fig. 3.1. Schematic representation of a magnet sector anaiyser. For a given source potentiai Vant magnetic fieid B, oniy ions of one m/z wiii be defiected aiong the correct radius rand strike the detector.

Raise the knee to take a further cut and repeat until aU the surface is produced at the correct radius. Since a vertical miUing machine is used, an alternative method of taking a cut can be used by lowering the spindle. 

Quality of maintenance of the tool (sufficient V-ring height and force, correct radius on die plate, correct punch and die clearance)... 

The volume coU of a single coil with this corrected radius of gyration then calculates to... 

Thus, if we know the radius of the ion, its charge, the change of its dielectric constant with temperature, and the temperature, we can calculate A//soivation- The following table compares the solvation enthalpies calculated from the Bom model with those enthalpies derived from experiment. The entry corrected radius is the radius of the cavity surrounding the ion, adjusted so as to reproduce solution thermochemistry ... 

Ion Corrected radius (nm) AHsoivation (Bom model) (kcal rnofr ) AHsoivation (Experiment) (kcal mol" )... 

To consider the geometrical magnification of the pipe image on film or IP in the tangential exposure technique according to the set-up shown in fig. 4 a correction of the measured wall thickness (w ) must be performed. The true wall thickness (w) depends in a rather complicated way on the film-focus-distance (f), the radius of the pipe (r) and the radius of the insulation (R) as shown in equation 2 ... 

It is to be noted that not only is the correction quite large, but for a given tip radius it depends on the nature of the liquid. It is thus incorrect to assume that the drop weights for two liquids are in the ratio of the respective surface tensions when the same size tip is used. Finally, correction factors for r/V < 0.3 have been determined, using mercury drops [37],... 

According to the simple formula, the maximum bubble pressure is given by f max = 27/r where r is the radius of the circular cross-section tube, and P has been corrected for the hydrostatic head due to the depth of immersion of the tube. Using the appropriate table, show what maximum radius tube may be used if 7 computed by the simple formula is not to be more than 5% in error. Assume a liquid of 7 = 25 dyn/cm and density 0.98 g/cm. ... 

STM and AFM profiles distort the shape of a particle because the side of the tip rides up on the particle. This effect can be corrected for. Consider, say, a spherical gold particle on a smooth surface. The sphere may be truncated, that is, the center may be a distance q above the surface, where q < r, the radius of the sphere. Assume the tip to be a cone of cone angle a. The observed profile in the vertical plane containing the center of the sphere will be a rounded hump of base width 2d and height h. Calculate q and r for the case where a - 32° and d and h are 275 nm and 300 nm, respectively. Note Chapter XVI, Ref. 133a. Can you show how to obtain the relevent equation ... 

L is Avagadro s constant and k is defined above. It can be seen that there are indeed two corrections to the conductivity at infinite dilution tire first corresponds to the relaxation effect, and is correct in (A2.4.72) only under the assumption of a zero ionic radius. For a finite ionic radius, a, the first tenn needs to be modified Falkenliagen [8] originally showed that simply dividing by a temr (1 -t kiTq) gives a first-order correction, and more complex corrections have been reviewed by Pitts etal [14], who show that, to a second order, the relaxation temr in (A2.4.72) should be divided by (1 + KOfiH I + KUn, . The electrophoretic effect should also... 

A. rather complex procedure is used to determine the Born radii a values of which. calculated for each atom in the molecule that carries a charge or a partial charge. T Born radius of an afom (more correctly considered to be an effective Born radii corresponds to the radius that would return the electrostatic energy of the system accordi to the Bom equation if all other atoms in the molecule were uncharged (i.e. if the other ato only acted to define the dielectric boundary between the solute and the solvent). In Sti force field implementation, atomic radii from the OPLS force field are assigned to ec... 

The Is orbital /i = is correct but not normalized. The normalized function governing the probability of finding an electron at some distance r along a fixed axis measured from the nucleus in units of the Bohr radius oq = 5.292 x 10 " m is... 

The supporting medium was water at 298 K (p = 0.99727), and the density of latex is 1.2049 g cm . The latex particles had an average radius of 2.12 x 10 mm hence, their effective mass corrected for buoyancy is their volume times the density difference Ap between latex and the supporting medium, water... 

Calculating nonbonded interactions only to a certain distance imparts an error in the calculation. If the cutoff radius is fairly large, this error will be very minimal due to the small amount of interaction at long distances. This is why many bulk-liquid simulations incorporate 1000 molecules or more. As the cutoff radius is decreased, the associated error increases. In some simulations, a long-range correction is included in order to compensate for this error. 

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